Resistors in series
Current
When resistors are connected in series, the current through each resistor is the same.
In the circuit below: IS = I1 = I2 = I3
Voltage V (or potential difference)
When resistors are connected in series, the total of all the voltages (sometimes referred to as potential difference) across each component is equal to the voltage across the power supply.
In the circuit above:
VS = V1 + V2 + V3
This is just a form of the law of conservation of energy.
The supply voltage is a measure of the energy supplied to each Subatomic particle, with a negative charge and a negligible mass relative to protons and neutrons..
The voltage across each component is the electrical energy converted by each component.
Therefore, the energy supplied equals the energy converted 鈥 energy has not been created or destroyed in the circuit.
Resistance
The total resistance R of two or more An electrical component that restricts the flow of electrical charge. Fixed-value resistors do not change their resistance, but with variable resistors it is possible to vary the resistance. connected in series is the sum of the individual resistances of the resistors.
For the circuit above the total resistance R is given by:
R = R1 + R2 + R3
Example
Find the total resistance of the circuit above.
Answer
This is a series circuit and so total resistance is found using the equation:
R = R1 + R2 + R3 + R4
R = \({4}\Omega + {8}\Omega + {2}\Omega + {12}\Omega\)
R = \({26}\Omega\)
The total resistance of the network of resistors is \({26}\Omega\). This means that the four individual resistors can be replaced by one resistor of \({26}\Omega\).
Adding resistors in series always increases the total resistance.
The current has to pass through each resistor in turn so adding an additional resistor adds to the resistance already encountered.
Resistors in parallel
Current
When resistors are connected in parallel, the current from the power supply is equal to the sum of the currents through each branch of the circuit.
In other words, the currents in the branches of a parallel circuit add up to the supply current.
In the circuit above:
IS = I1 + I2 + I3
This relationship expresses the law of conservation of charge.
All electrons that set out from the supply must return to the supply and each electron can only pass through one parallel branch.
Voltage
In a parallel circuit, the voltage across each branch of the circuit equals the supply voltage.
For the circuit above:
VS = V1 = V2 = V3
Resistance
When resistors are connected in parallel, total resistance, R, is calculated using the equation:
\(\frac{1}{R}=\frac{1}{R}_{1}+\frac{1}{R}_{2}+\frac{1}{R}_{3}\)